5. \(\mathbf { A } = \left( \begin{array} { r r } - 4 & a
b & - 2 \end{array} \right)\), where \(a\) and \(b\) are constants.
Given that the matrix \(\mathbf { A }\) maps the point with coordinates \(( 4,6 )\) onto the point with coordinates \(( 2 , - 8 )\),
- find the value of \(a\) and the value of \(b\).
A quadrilateral \(R\) has area 30 square units.
It is transformed into another quadrilateral \(S\) by the matrix \(\mathbf { A }\).
Using your values of \(a\) and \(b\), - find the area of quadrilateral \(S\).